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Prove cosA-sinA+1/cosA+sinA-1=cosecA+cotA

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Prove cosA-sinA+1/cosA+sinA-1=cosecA+cotA

Posted by Alisha Singh 4 years, 6 months ago

CBSE > Class 10 > Mathematics

2 answers

Siya Singhal 4 years, 5 months ago

LHS=cosA+sinA−1cosA−sinA+1 dividing Nr and Dr by sinA we get, =sinAcosA+sinAsinA−sinA1sinAcosA−sinAsinA+sinA1 =cotA+1−cosecAcotA−1+cosecA =cotA+1−cosecAcotA+cosecA−(cosec2A−cot2A) =cotA+1−cosecA(cotA+cosecA)(1−cosecA+cotA) =cotA+cosecA=RHS

Balaji B 4 years, 6 months ago

Multiplying the numerator and denominator with sinA : SinA [CosA – SinA +1]/ SinA [CosA + SinA –1] SinACosA–Sin^2A+SinA/ SinA [CosA +SinA –1] SinACosA+SinA –[1–Cos^2A]/ SinA[CosA+SinA–1] SinACosA+SinA–[(1–CosA)(1+CosA)] / SinA[CosA+SinA–1] SinA[CosA+1]–[(1–CosA)(1+CosA)] / SinA [CosA + SinA–1] (CosA+1)(SinA–1+CosA)/ SinA (CosA + SinA–1) (CosA+1)(SinA+CosA—1)/ SinA (CosA+SinA–1) (CosA+SinA–1) will get cancelled So , CosA+1/SinA is left Dividing (CosA) and (1) individually by (SinA), we get CotA + CosecA Which is equal to R.H.S Hence Proved

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